mlsanityData to 14 Oct 2026

Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios

arXiv 2205.07731 ↗First posted 16 May 2022cs.CEcited by 46

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Abstract (arXiv)

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial differential equations (PDEs) via embedding physical laws into the loss function. Many inverse problems can be tackled by simply combining the data from real life scenarios with existing PINN algorithms. In this paper, we present a multi-task learning method using uncertainty weighting to improve the training efficiency and accuracy of PINNs for inverse problems in linear elasticity and hyperelasticity. Furthermore, we demonstrate an application of PINNs to a practical inverse problem in structural analysis: prediction of external loads of diverse engineering structures based on limited displacement monitoring points. To this end, we first determine a simplified loading scenario at the offline stage. By setting unknown boundary conditions as learnable parameters, PINNs can predict the external loads with the support of measured data. When it comes to the online stage in real engineering projects, transfer learning is employed to fine-tune the pre-trained model from offline stage. Our results show that, even with noisy gappy data, satisfactory results can still be obtained from the PINN model due to the dual regularization of physics laws and prior knowledge, which exhibits better robustness compared to traditional analysis methods. Our approach is capable of bridging the gap between various structures with geometric scaling and under different loading scenarios, and the convergence of training is also greatly accelerated through not only the layer freezing but also the multi-task weight inheritance from pre-trained models, thus making it possible to be applied as surrogate models in actual engineering projects.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 May 2022.

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Citing papers per year: 2022: 2; 2023: 10; 2024: 12; 2025: 16; 2026: 6.

46 papers.

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  1. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 131
  2. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 101
  3. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  4. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 31
  5. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  6. 2023Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networkscited by 18
  7. 2023A practical PINN framework for multi-scale problems with multi-magnitude loss termscited by 15
  8. 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domainscited by 15
  9. 2025Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptationcited by 15
  10. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 11
  11. 2024A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformationscited by 10
  12. 2025Sub-Sequential Physics-Informed Learning with State Space Modelcited by 10
34 more
  1. 2024Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learningcited by 9
  2. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  3. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  4. 2023Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticitycited by 7
  5. 2022Physics Informed Neural Network for Dynamic Stress Predictioncited by 6
  6. 2023Challenges and opportunities for machine learning in multiscale computational modelingcited by 6
  7. 2024Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equationscited by 5
  8. 2022Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Datacited by 4
  9. 2024Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equationscited by 4
  10. 2023iPINNs: Incremental learning for Physics-informed neural networkscited by 3
  11. 2024Solving Differential Equations with Constrained Learningcited by 3
  12. 2024Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEscited by 3
  13. 2025Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometriescited by 3
  14. 2025iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filtercited by 3
  15. 2025ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariancecited by 2
  16. 2026A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentialscited by 2
  17. 2024Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanicscited by 1
  18. 2025Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulencecited by 1
  19. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  20. 2025A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beamcited by 1
  21. 2023Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEscited by 0
  22. 2024A Hybrid Approach of Transfer Learning and Physics-Informed Modeling: Improving Dissolved Oxygen Concentration Prediction in an Industrial Wastewater Treatment Plantcited by 0
  23. 2025Conformal mapping based Physics-informed neural networks for designing neutral inclusionscited by 0
  24. 2025Rigid Body Adversarial Attackscited by 0
  25. 2025The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problemscited by 0
  26. 2025On-site estimation of battery electrochemical parameters via transfer learning based physics-informed neural network approachcited by 0
  27. 2025Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networkscited by 0
  28. 2025Toward using explainable data-driven surrogate models for treating performance-based seismic design as an inverse engineering problemcited by 0
  29. 2025IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimationcited by 0
  30. 2026PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturingcited by 0
  31. 2026Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Datacited by 0
  32. 2026Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networkscited by 0
  33. 2026Generalized PINN-Based Inverse Estimation of Spatially Varying Heat Transfer Coefficients with Transfer Learningcited by 0
  34. 2026Continuous-Time Cloth Dynamics with Physics-Informed Neural ODEscited by 0